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MONT 105N -- Analyzing Environmental Data\\
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Midterm Examination -- April 12, 2013
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Your Name:  $\underline{\qquad\qquad\qquad\qquad\qquad\qquad}$
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{\it Directions:}  Do all work on these sheets.  You may use the back if necessary, but please
alert me with a note if you do.  In a case where a later part of a question depends on a previous
part, I will give credit for the later part as long as you have a correct approach, even without
the correct value from the previous part.  There
are 100 points, distributed as indicated in the questions.
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I.  A fertile but short-lived organism has monthly fertility and survival rates
as given in this table:
$$
\begin{array}{llccc}
{\rm Age group} & \vline & A & B & C \\ \hline
{\rm Age (months)} & \vline & 0-1 & 1-2 & 2-3\\
{\rm Fertility rate} & \vline & 0 & 4 & 3\\
{\rm Survival rate} & \vline & 0.3 & 0.1 & 0.0 
\end{array}
$$
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A)  (10) Draw the corresponding life-cycle graph.
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B)  (10) Convert the information in the table (and the life-cycle graph) to 
a system of difference equations.
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C)  (5) Given that $a(0) = 300$, $b(0) = 200$ and $c(0) = 100$, determine 
$a(1),b(1),c(1)$.  
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II.  All parts of this question refer to the following data set with $n = 9$:
$$12, 15, 18, 25, 26, 28, 31, 33, 34$$
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A)  (10) Find the ``5-number summary'' and draw the corresponding box plot.
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B)  (5)  Is the Bowley measure of skewness positive or negative for this data set?
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C)  (5)  Given that the SD is approximately $SD = 7.97$, how well does the 
Empirical Rule ``fit'' this data?  (Say what that rule says and then determine how
closely this data follows it.)
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III.  Suppose that a data set of $n = 25$ Dungeness crab shell 
length measurements has been collected.
The mean shell width in the sample is $\overline{x} = 20$cm  and the SD is $4$cm.
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A) (5)  Would the $z$-score of a measurement $x = 18$ be?
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B) (5)  What width measurement would correspond to a $z$-score of $-1.3$?
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C) (5)  Find a $95\%$ confidence interval for the population mean shell width.
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D) (10)   Estimate the proportion of the population of crabs with shell widths
between $18$ and $21$cm.  State any assumptions you are making to arrive at your estimate.
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IV.  Essay.  (30)  Exactly what is the ``hockey stick'' graph?  How was it originally generated?  
When and where did it first appear in the published scientific record?   Have other studies 
confirmed this general pattern or called into question
the original conclusions?   When and why did the ``hockey stick'' become such a 
contentious issue in the climate change 
debate?  What is the IPCC and what do they do?  What was the role of the IPCC here?
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